Followed the procedure entodoays described. Got stuck when creating a disk image with Ubuntu Disks. Did a little research:
- managed to do dd of all partitions (sdb1..sdb10) withot problems,
- failed to do dd of "unused space" at the beginning of the drive, stuck at 9,4 MB (or 13,4 MB if conv=noerror used),
- badblocks reported 4 bad blocks (9600-9603) when doing read-only test on /dev/sdb

So I am out of luck I guess. I can still try and overwrite existing partitions 1..10 by the ones from working device but having those bad blocks is not something I wanted to see.

I wrote to Sony Listens about my case, I wonder what they will do. Usually they understand the situation and do something good